Question: Assume that in a given country, tax revenues, T, depend on income, I, according to the formula
T = - 4,000 + 0.21
Thus, for example, when a household has an income of $50,000, its tax burden is -4,000 + 0.2 X 50,000, or $6,000. Is this a progressive tax schedule? Now let's generalize the tax schedule in this problem to:
T= a + tI
where a and t are numbers. (For example, in the tax schedule above, a = -4,000 and t = 0.2.) Write down a formula for the average tax rate as a function of the level of income. Show that the tax system is progressive if a is negadve, and regressive if a is positive.
[Hint: The aver-age tax rate is TH.]